Pythagorean Triples

Three whole numbers
a
,
b
,
c
which satisfy the equation of the
Pythagorean Theorem
(
a
2
+
b
2
=
c
2
) are called
Pythagorean triples
. A few of the smallest ones are shown in the table below. Each Pythagorean Triple corresponds with a right triangle whose side lengths are in whole-number ratios.

Pythagorean Triples

3
,
4
,
5

3
2
+
4
2
=
5
2
9
+
16
=
25

6
,
8
,
10

6
2
+
8
2
=
10
2
36
+
64
=
100

5
,
12
,
13

5
2
+
12
2
=
13
2
25
+
144
=
169

8
,
15
,
17

8
2
+
15
2
=
17
2
64
+
225
=
289

Note that once you have one Pythagorean triple, you can get many more: just multiply all
3
numbers by a constant. For instance, from
3
,
4
,
5
, we get the family of triples: